# Spin-orbit-coupling induced localization in the expansion of an interacting Bose-Einstein condensate

## TL;DR

This paper investigates how spin-orbit coupling affects the expansion of a Bose-Einstein condensate, revealing a slowdown near phase transitions due to increased effective mass and resulting in localized behavior.

## Contribution

The study introduces a hydrodynamic formalism to analyze spin-orbit coupled BEC expansion, highlighting the impact of phase transitions on dynamics and localization effects.

## Key findings

- Expansion slows down near phase transition
- Effective mass increases significantly
- Emergence of local spin polarization

## Abstract

By developing a hydrodynamic formalism, we investigate the expansion dynamics of the single-minimum phase of a binary spin-orbit coupled Bose-Einstein condensate, after releasing from an external harmonic trap. We find that the expansion of the condensate along the direction of the spin-orbit coupling is dramatically slowed down near the transition between the single-minimum phase and the plane-wave phase. Such a slow expansion, resembling a form of an effective localization, is due to the quenching of the superfluid motion which results in a strong increase of the effective mass. In the single-minimum phase the anisotropic expansion of the Bose gas, which is spin balanced at equilibrium, is accompanied by the emergence of a local spin polarization. Our analytic scaling solutions emerging from hydrodynamic picture are compared with a full numerical simulation based on the coupled Gross-Pitaevskii equations.